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revision 1st sec.
Final revision 1st sec. 2nd term alg. The quadratic equation ax2 + bx + c = 0 b,c ∈R , a≠0 . If L & M are the roots of the quadratic equ. So:F(L) = 0 , (x – L) is a factor of the equ. F(M) = 0 , (x – M) is a factor of the equ. The formula The discriminate is If The discriminate is –ve then the equation has no real roots. If The discriminate is +ve then the equation has two fifferent roots. If The discriminate is 0 then the equation has two equal roots.(one root ) If L & M are the roots of the quadratic equ. So: The sum of the roots (L + M) = The product of the roots (L M) = The quadratic equation is x2 – (the sum of the roots) x + the product of the roots = 0 Or (x – L)(x – M) = 0 1)If a = 1 then (L + M ) = -b , LM = c 2) if b = 0 , then L + M = 0 è L = -M 3) If a = c , then the equ. è ax2 + bx + a = 0 Then LM = 1 è L = 1) COMPLETE: 1) if x = 3 is a root of x2 – 8x + c = 0 , then c = ……. 2) if (x – 2) is a factor of x2 – 5x + 6 , then f(2) = …….. 3) if f(x) = 2x2 + bx + 9 & f(-2) = 15 , b = … 4) if f(x) = 2x2 +7x – 15 , then f(x) = 0 when x = ……..
5) if 3x2 – 9 = 0 , then the sum of the two roots = ……… & their product = ………… 6) if one of the roots of the equ, x2 + (k-5) x – 9 = 0 is the a. inverse of the other , then k = … 7) if the sum of the two roots of the equ. 2x2 – 3x + 5c = 0 equals their product , then c = ……. 8) the quadratic equ. Whose two roots are 3 & 5 , is ………… 9) the quadratic equ. Whose two roots are 2/3 & 3/2 , is ………… 10 ) if x = 3 is a root of x2 – 8x + c = 0 , then the other root is ….. 11) the product of the roots of the equ. 3x + 4 = 2x2 equals ………….. 12) if one root of the equ. X2 + 5x + (k – 3) = 0 is the m.inverse of the other. Then k = ………. |
#2
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جزاك الله خيرا
مشكور علي مجهودك |
#3
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iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii iiii
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#4
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ششششششششكككككككررررررررراااااااااااااااااااااااااا ااااااا
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#5
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مشكووووور اخي الفاضل
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#6
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شكرااااااااا
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#7
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Thank you
for your effort |
العلامات المرجعية |
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